Density of States for Warped Energy Bands

An angular effective mass formalism previously introduced is used to study the density of states in warped and non-warped energy bands. Band warping may or may not increase the density-of-states effective mass. Band "corrugation," referring to energy dispersions that deviate "more severely" from being twice-differentiable at isolated critical points, may also vary independently of density-of-states effective masses and band warping parameters. We demonstrate these effects and the superiority of an angular effective mass treatment for valence band energy dispersions in cubic materials. We also provide some two-dimensional physical and mathematical examples that may be relevant to studies of band warping in heterostructures and surfaces. These examples may also be useful in clarifying the interplay between possible band warping and band non-parabolicity for non-degenerate conduction band minima in thermoelectric materials of corresponding interest.